What is the answer to the following question:?

Question

This is the question:
"There are 10 students in Mr.Alvarez's art class. Throughout the year, each student must pair up with every other student to complete a project. How many projects will be completed?"
Thanks so much for helping me.
P.S can you tell me the format to solve this question

Answer 1

It's a combination problem.
You have 10 students and you are picking two at a time. In how many ways can that be accomplished?
C(10,2) = 10*9/2 = 45

Answer 2

I am one student in this class. I must pair up with a total of nine other students during the year. (Every other student--> 10 - 1 = 9)

This means I will pair up 9 times at one project each time for a total of 9 projects with my name on them.

There are 10 students, 2 per project, so 10 / 2 = 5 pairs of students (teams) per project.

9 projects assigned times 5 teams = 45 total projects created during the year.

Answer 3

My answer is 900
If each student pairs up 9 times ( a student cannot pair up with himself), therefore 9 times 10 = 900

10 - 1 times 10 = 900

Answer 4

its 10* 10
because there are 10 students and each student have to do it 10 times .. one student do the project 10 times .. so we have to find How many projects will be completed if 10 students do it

so its 10*10
= 100 .. ok


it means they finish 100 projects

Answer 5

You have 10 students and you want to know all the ways to choose 2 of them.

The formula is "N-choose-R" or 10choose2 here.

You also need to know what 'factorial" means.

For instance 4! means "4-factorial" and it equals 4*3*2*1
7! would be 7*6*5*4*3*2*1 etc.

NchooseR = (N!) / [R! * (N - R)!]
10choose2 = (10!) / (2! * 8!)
= (10*9)/(2*1) = 45 possible pairs

Answer 6

9+8+7+6+5+4+3+2 = I think that's right.

Answer 7

It's 44 - Eric L was right.